Problem: Solve for $k$, $ \dfrac{2k - 9}{k + 3} = -\dfrac{10}{4k + 12} + \dfrac{3}{k + 3} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $k + 3$ $4k + 12$ and $k + 3$ The common denominator is $4k + 12$ To get $4k + 12$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ \dfrac{2k - 9}{k + 3} \times \dfrac{4}{4} = \dfrac{8k - 36}{4k + 12} $ The denominator of the second term is already $4k + 12$ , so we don't need to change it. To get $4k + 12$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{3}{k + 3} \times \dfrac{4}{4} = \dfrac{12}{4k + 12} $ This give us: $ \dfrac{8k - 36}{4k + 12} = -\dfrac{10}{4k + 12} + \dfrac{12}{4k + 12} $ If we multiply both sides of the equation by $4k + 12$ , we get: $ 8k - 36 = -10 + 12$ $ 8k - 36 = 2$ $ 8k = 38 $ $ k = \dfrac{19}{4}$